You could just trust him 😉
SERIOUSLY, short of getting a report from someone on-site that you trust, no software can be fully trusted. Any software can be bypassed or manipulated. and just showing your lack of trust by using tracking software might be the motivation needed for him to justify manipulating it.
How about negotiating some other metric, like a short daily summary which, along with copies of code completed, that will satisfy you he has worked the hours he claims.